Map projections
Map projection is "the process of systematically transforming positions on
the Earth's spherical surface to a flat map while maintaining spatial
relationships. This process is accomplished by the use of geometry or, more
commonly, by mathematical formulas. Map projection can be best visualized by
imagining a light bulb placed at the centre of a transparent globe and having
its lines of longitude and latitude cast upon either a flat sheet of paper or a
sheet of paper rolled into a cylinder or cone placed over the globe." (from Atlas of Canada: map projection).

A good text for beginners to consult the
text concerning scale and map projection from Arthur H. Robinson's et
al. book Elements of cartography (6th ed., New York, 1995).
For a more sophisticated approach one can use the unit on ,
which is part of Brian Klinkenberg'sGIS and Cartography Online
Resources with the University of
California at Santa
Barbara.

For those converting analogue to digital the following publications
are available:

A more recent online edition of this publication with a
zipped file which contains the entire text of USGS
Bulletin 1856, Bibliography of Map Projections, edited by John
P. Snyder with Harry Steward and published in 1988. John Snyder has since
corrected, supplemented, and renumbered the text in 1994 and 1996. It is also
converted from a coded file, which can be printed with all the diacritical
marks in the various languages on an Epson printer using a homemade word
processor, to HTML codes to permit reading of all diacriticals allowed on the
Internet. The exceptions are diacriticals used only in Eastern European
languages, which are removed and the letter shown without a diacritical, except
that the Hungarian double accent acute is made an umlaut. He also has the
Bibliography in a Microsoft Word file, so that all Eastern- and Western-European
diacriticals, as well as new insertions of Russian Cyrillic following the
transliterations already included, may be displayed in the printed form or on
the screen.
The USGS upkeeps the site Map
projections, which contains a description and visualisation of 17 main
projections, a summary of projection properties, and a summary of areas
suitable of mapping with projections.
Some of these projections are also illustrated on Zbigniew
Zwolinski's 'The Great Globe Gallery'.

With the computerization of cartography the amount of projections
proliferated and fortunately also the Internet-resources available. The
following sources are multiple sources with many hyperlinks to other documents
or web-sites.

At this map
projection homepage you will find a collection of information relating to
map projections. This Home Page was inspired by a seminar in map projections in
the Geography Department, Hunter College,
City University of New York, led by Dr. Keith C. Clarke ,
Geography Department, UCSB.

Other extensive home pages are the
Map Projection Overview by Peter H. Dana of the Department of Geography, University
of Texas at Austin,
and the European
Map Projections by Stefan A. Voser of the Institut für Geodäsie, Universität
der Bundeswehr München.

Bar scale values
Scale is "A ratio representing the relationship between a specified
distance on a map and the actual distance on the ground. For example, at the
scale of 1:50 000, 1 unit of
measurement on the map equals 50 000 units of the same measurement on the
ground. Map scale is frequently expressed as a representative fraction and
graphically as a bar scale" (from :
Scale).

Herman Wagner (1840-1929) gives a large historical expose
concerning scales in "The mapscale" (Der Kartenmaßstab. In:
Zeitschrift der Gesellschaft für Erdkunde zu Berlin.
1914. pp. 1-34, 81-117), where he connects the use of the
scale with the projection used. Knowing this one must always be aware
that a certain scale (being it a scale bar or a representative fraction) only
gives true values on but a small part of a map. Depending on the kind of
projection the deviation will be larger or smaller, also keeping in mind
whether it is a large scale or small scale map one is viewing.

To calculate the distance between two cities using the great
circle method (as the crow flies) one needs to know latitude and longitude of the two places. Bali and
Indonesia on the net provides a distance calculator using geographic
placenames. It does the arithmetics based on the 'PROJ' system available from
the U.S. Geological Survey, when necessary supported by a locational map, and a
travel map with driving directions. It also shows the compass headings between
the two cities.
Another easy to use programme is the Great
Circle Calculator. Here one should, however, fill in the right geographical
co-ordinates for latitude and longitude. The result will be a distance in miles
or kilometres. There are no auxiliary services. For those interested in these
calculations a query on distance
"great circle" on the search-engine Google will result in 21,600
hits.

Trying to give scales for pre-1800 maps implies always 3 to
4 measurements and should result in phrases as 'Scale varying from [ca.
1:7,400] to [ca. 1:8,400]' when derived from measurements on modern maps.
Or 'Scale [ca. 1:7,900], measurement derived from scale bar (900 rods = 33
mm)'. When the scale bar is not used in this way its mention should be
relegated to the notes.
I advise curators and editors of facsimiles to be careful with scales and never
to use one scale denominator when the map does not have a
geometrical basis based on triangulation. When the cataloguer is not sure it is
better to state 'Scale unknown' and give a scale-bar note than
giving a quizzing approximation with which nothing can be proved or which
creates confusion.

When the calculation of a scale is dependent on a grid of
geographic co-ordinates one should measure the distance between two succesive
parallels (1º = 111.11 km or 60 nautical miles, 1' = 1.85 km or 1 nautical
mile) using a meridian, when possible in the middle of the map.

For those not used to calculating scales Terry Reese has
created the site Scale
calculator, which allows for American standard, metric, and miscellaneous
conversions.

In Petermanns geographische Mitteilungen
(1855-2004), a famous German geographical journal, almost every map contains a
scale denominator as well as a scale bar. The scale bar denominates a certain
value per 1° longitude at the equator. The longitudinal measurement of 1°
longitude at the equator is 111,324 kilometres or 60 nautical miles.
As there are some very exotic local scale bars which might be unknown the
following table gives the values (in order of precision, as used in Petermann)
ordered by the English name of the country in which the value is used. It may
be that a bar scale is wrongly attributed to a certain country or area as they
have to be interpreted from the German or do not have any explication of their
origin.
Some values are only related to specific maps [i.e. 4,000 pied = 20 mm] and
thus do not give any objective measure. They are included, however, to show
their existence. Numbers in Bold under the heading '1
degree' are most used on the maps.
Only verbatim statements from Petermann are used and in no way are
measures recalculated.

Geoff Armitage's Conversion table
of measurements
Geoff Armitage of the British Library Map Library in the past years has created
a conversion table into millimetres of measures appearing in the British
Library map catalogues. I am greatly indebted to him to be able to enrich this
document with his table.

GEOFF ARMITAGE'S CONVERSION TABLE OF MEASUREMENTS

Name of Measure

Approx. Equivalent in millimetres

Antwerp ruthen

5,736

Aunes

1,143

Baras castellanes

835

Bolognese foot

380

Brabant foot

281

Bracas

2,200

Braccia

600

Brasse

595

Brazos castellanas

1,683

Brazza

595

British fathom

1,828

Cable

219,456

Calemberger foot

292

Calemberger ruthen

4,672

Canne

2,000

Canne anconitane

2,000

Canne napolitane

2,096

Canne romane

2,112

Canne siciliane

2,028

Carmi

2,000

Castilian league

6,350,500

Castilian varas

835

Chain

20,117

Cleffter

2,000

Common league

7,408,900

Dutch league

5,969,990

Dutch mile

1,000,000

English league

4,828,032

Faden

1,629

Fathom

1,828

Florentine braccia

583

Florentine mile

1,778,000

Foot

305

French foot

330

French league

4,448,200

French marine league

5,556,700

French pace

812

French toise

1,949 (post-1812: 2,000)

Genevese toise

2,599

Geometrical foot

337

Geometrical pace

1,524

German mile

7,649,000

Irish perch

6,400

Italian mile

1,852,200

Italian pace

1,500

Kilometre

1,000,000

Klaffter

2,000

Lachter

2,036

League

4,828,032

Leucarum Hispanicarum [= Spanish
league???]

6,300,000

Lieue [= league]

4,828,032

Lieue commune de France

4,445,400

Lieue japonaise

???

Lieue marine

5,556,700

Marine league

5,556,700

Marine mile

1,852,200

Metre

1,000

Mexican league

4,190,000

Mexican varas

848

Milanese mile

1,652,600

Mile

1,609,344

Miliarium/milliaria [= English
mile]

1,609,344

Mille (itineraire)

1,949,000

Mille marin

1,852,200

Milliaria anglica [= English
mile]

1,609,344

Milliaria germanica [=German
mile]

7,649,000

Milliaria Italica [= Italian
mile]

1,852,200

Milliaria thietm. [= Thietmarsh mile ???]

???

Modenese perch

3,180

Nautic[al] mile

1,852,200

Pace

762

Palmi

250

Palmi genovese

249

Palmi romani

228

Paraguay league

4,190,000

Paris foot

330

Pas [= French pace]

812

Passi

1,500

Pedum [= Foot???]

305

Perch

5,029

Perticarum [= Perch]

5,029

Pertiche ferrarese

4,038

Pertiche modenese

3,180

Pertiche versonese

2,057

Piedmontese mile

1,778,000

Pole

5,029

Rhenish/Rheinland/Rynland -
rod/ruthen/roeden

3,766

Rhenish foot

314

Rhenish verge/yard

3,766

Rhinesee Rhenish

Rod

5,029

Roden/Danish perches??? (La
Rode)

3,138

Roman palmi

228

Russian faden/fathom

1,629

Russian toise

1,604

Rynland see Rhenish

Scala [ignore; note the next
word]

Schrit[te]

1,710

Schuh [= German foot???]

290

Scots chain

22,676

Sea league = marine league???

5,556,700

Sea mile = nautic[al]
mile???

1,852,200

Spanish league

6,300,000

Spanish maritime league

5,566,700

T. [= Toise]

2,000

T[h]oise

2,000

Trabocci/Trabucchi

3,000

Trabocchi of Piacenza

2,819

Varas
[Castellanas/Castille/Espanolas/Spanish]

858

Venetian mile

1,738,700

Venetian pasa/pace

1,739

Verge de Rhin[land]

3,766

Veronese mile

1,778,000

Werst

1,066,780

Yard

914

As an aid to research and cataloguing the
following table contains publications which concern measures etc.
Should there be more than one significant publication in a country they are,
when possible, organized from the general to the specif ic.

Based on published works between 1830-1840. All measures are converted to the decimal
system and, where necessary, to other universal measures. Measures are
usually regionally subdivided to area of origin. Also locally used
designations are included with reference to the french designation (FRENCH)

Some 4,000 terms are identified
in familiar English alphabetic order and related to their fellow units within
their culture and to corresponding terms of adjacent and other interacting
peoples. With index by country. (ENGLISH)

Linear measures encountered in
the alphabetical listing are in Russian, with the Latin given in parenthesis
in those cases where the Russian transliterates differently from the
original. Some exotic measures are encountered, like the British 'nail' (5.71
cm) and American 'place' (76.2 cm). Measures arranged by country and
alphabetically. (RUSSIAN)

For good measure : a complete compenduim of international weights and measures / William
D. Johnstone. - New York : Holt, Rinehart
and Winston, [ca. 1975]. - XXII, 329 p. - ISBN 0-03-013946-5

Part one: Units of length (pp.
1-57)
Part five: the metric system and conversion tables (pp. 208-212) (ENGLISH)

English systems: linear systems
(pp. 5-54). Measures are given in two historical tables, 1305-1826 and
1826-present. Metric equivalent is given.
French systems (New France): linear systems (pp. 75-80). This gives the time
periods in which the systems were in use, with metric equivalents.
American systems: pp. 87-90.
Canadian systems: pp. 91-100, giving measures used in the Dominion as well as
in the provinces.
(ENGLISH)

Geographical co-ordinates
Though Greek philosophers like Pythagoras, Aristoteles, and Erathosthenes
already posed that the earth was spherical it was the famous Greek astronomer
Hipparchos (ca. 190 - 125 B.C.) who thought to cover this sphere with a grid of
meridians and parallels. Following the Babylonian use of dividing circles and
angles according to the sexagesimal system he created a grid of 360 lines
running from the North to the South Pole and 180 lines running parallel to the
equator. The lines running from the North to the South Pole later were called
meridians, because when two places had the same time at noon they were on the same meridian, after the Latin
'meridies'.

For a general and mathematical overview there is the Coordinate
Systems Overview by Peter H. Dana of the Department of Geography, University
of Texas at Austin.

Looking for ways for coordinate conversion and
transformation the site Cartographic
links for botanists compiled by Raino Lampinen, Botanical
Museum, Finnish
Museum of Natural History, contains
mapping software packages, which have various utilities for coordinate
conversion.

For geographic coordinate transformation pertaining to the Dutch
grid and vice versa one can use the website Transformatie
van RD-coördinaten en geografische coördinaten created by Ed. Stevenhagen.
(There is also a Java-script
with maps where the location is indicated). Besides it automatically gives the
coordinates in WGS84 and the meridian-convergence.

In 1761 John Harrison (1693-1776) solved the longitude
problem when his Model No. 4 or "H. 4" chronometer was used on a
nine-week trip from London to Jamaica.
During this trip his clock only lost five seconds, or about 1.25 minutes of
longitude. His "K. 1" clock was successfully tested by James Cook on
his second voyage around the world, beginning in 1772. (Boorstin, Daniel J.
(1991). The discoverers.Vol. 1, p.
86.).
Connected to the problem of the prime-meridian is that of it's opposite, the
date line. From a Western point of view this was always situated somewhere at
its antipode, as fictitionally treated by Umberto Eco in his The
island of the day before (originally published as L'isola del
giorno prima, 1994). A more scientific treatment of this problem can be
found on A
History of the International Date Line by Robert H. van Gent.

As the position of prime meridians is not always known I
reproduce here a table in use with the CCK (Dutch Union Map Catalogue),
ammended with information from other sources, among others Cartographic
materials : a manual of interpretation for AACR2. The position is given
with respect to the (Greenwich)
International Prime Meridian, adopted at the 1884 International Meridian
Conference at Washington DC,
USA.

For those having trouble calculating bounding-box coordinates for maps the tool from Klokantech.com comes in very handy, especially since the coordinates are given in any MARC- or other description-format one is working with.

LOCATION OF PRIME MERIDIANS

City

Country

Position

Alexandria

Egypt

Used by Albert Hermann in 1930
for a reconstruction of a map of Marinus of Tyrus. The meridians are hours
west or east of Alexandria

Amersfoort

Netherlands

E 005º23'

Amsterdam

Netherlands

E 004º53'01"

Antwerp

Belgium

E 004º22'50"

Athens

Greece

E 023º42'59"

Batavia (Jakarta)

Indonesia

E 106º48'28"

Berlin

Germany

E 013º23'55"

Berne

Switzerland

E 007º26'22"

Bogota

Colombia

W 074º04'53"

Bombay

India

E 072º48'55"

Brussels

Belgium

E 004º22'06"

Bucharest

Romania

E 026º07'

Cádiz

Spain

W 006º17'42"

Canberra

Australia

E 149º08'

Capetown

South-Africa

E 018º28'41"

Caracas

Venezuela

W 066º55'50"

Celebes, Middle Meridian of

Indonesia

E 121º48'

Christiana (Oslo)

Norway

E 010º43'23"

Copenhagen

Denmark

E 012º34'40"

Córdoba

Argentina

W 064º12'03"

Ferro

Canary Islands

W 017º39'46"

Greenwich

United
Kingdom

E 000º00'00"

Genoa

Italy

E 008º55'

Helsinki

Finland

E 024º57'17"

Istanbul

Turkey

E 028º58'50"

Jakarta

Indonesia

See: Batavia

Julianehaab

Greenland

W 046º02'22"

Kaliningrad

Russia

See: Köningsberg

Köningsberg

Russia

E 020º29'47"

Leningrad

Russia

See: St. Petersburg

Lissabon

Portugal

W 009º11'10"

London

United
Kingdom

W 000º05'43"

Madras

India

E 080º14'50"

Madrid

Spain

W 003º41'15"

Mexico City

Mexico

W 099º11'40"

Moscow

Russia

E 037º34'15"

Munich

Germany

E 011º36'32"

Naples

Italy

E 014º15'42"

New York
City (Manhattan)

United
States

W 074º00'29"

Oldenburg

Germany

E 008º12'

Oslo

Norway

See: Christiana

Padang, Sumatra

Indonesia

E 100º22'01"

Paris

France

E 002º20'14"

Peking

China

E 116º28'10"

Philadelphia

United
States

W 075º08'55"

Pulkovo (St. Petersburg)

Russia

E 030º19'39"

Quito

Ecuador

W 070º30'

Rio de
Janeiro

Brazil

W 043º01'21"

Rome

Italy

E 012º29'05"

Rotterdam

Netherlands

E 004º29'46"

San
Fernando

Spain

W 006º12'

San
Francisco

United
States

W 122º27'

Santiago

Chile

W 070º41'00"

Singkawang, Borneo

Indonesia

E 108º59'41"

South Sumatra

Indonesia

E 103º33'

St.
Petersburg

Russia

E 030º18'59"

Stockholm

Sweden

E 018º03'30"

Sucre

Bolivia

W 065º15'

Sydney

Australia

E 151º12'23"

Tenerife

Canary Islands

W 016º35'

Tirana

Albania

E 019º46'45"

Tokyo

Japan

E 139º44'40"

Washington (D.C.)

United
States

W 077º00'34"

When not taking into account which prime meridian is used
the following situation might occur.

HUMOR: Teaching Coordinates

The geography teacher was lecturing on map reading. After
explaining about latitude, longitude, degrees, minutes, and seconds, the teacher
asked, "Suppose I asked you to meet me for lunch at 23 degrees, 4 minutes,
30 seconds north latitude and 45 degrees, 15 minutes, zero seconds
east longitude."

After a confused silence, a voice volunteered, "I guess
you'd be eating alone."

(Ken Everard, on Maphist, 8 February 2001)

When the teacher meant GMT as prime meridian he would have
been lunching somewhere in the Arabian Desert called
Dawasir. Had the teacher meant e.g. the San Francisco
prime meridian he would have been lunching on a boat on the Great Bahama Bank
near Channel Rock!

Centesimal system of co-ordinates

(derived verbatim from: Cartographic
materials : a manual of interpretation for AACR2)
The sexagesimal division of the circle is now virtually universal in
cartographic work. However, in the 18th century French scientists, using the
metric system, devised the centesimal division of the circle. Today there exist
large numbers of maps of France
and its former colonial territories based on such a system. It can be quite
confusing due to the relative closeness of the values.
The centesimal division of the circle is extremely simple. The entire circle is
divided into 400 grads (a right angle in 90º in the sexagesimal system, 100
grads in the centesimal system). Each grad is in turn divided into 100 minutes
and each minute into 100 seconds. The centesimal values can be expressed in
regular decimal form or as minutes and seconds. The grad is shown as
"G" and the centesimal minutes and seconds have the same marks as the
sexagesimal ones, but with the slopes of the marks in the opposite direction.

The process of conversion is very simple.
It is known that 90º equals 100G and that
60 sexagesimal minutes or seconds equals 100 centesimal minutes or seconds.
Through a simple proportion multiply the centesimal values by 0.9 to obtain
sexagesimal degrees and the remainders are multiplied by 60 to obtain
sexagesimal minutes and seconds.

Equinox
The equinox is one of the two points of intersection of the ecliptic and the
celestial equator, occupied by the sun when its declination is 0º. This for
most map curators intangible phenomenon has been well described in Cartographic
materials : a manual of interpretation for AACR2
paragraph 3D2, p. 62-65. I refer those who are interested to this text as no
other source is available to me.